(10) Q3 Letter Carriers. A Canada Post letter carrier delivers mail to houses on a street. The number of mail items to be delivered to an individual house follows a Poisson distribution with mean = 1.3 and is independent from one house to another. The time taken to walk past a house for which there are no items requiring delivery is 15 seconds. The time taken to deliver items to a house is 15 seconds (plus the 15 seconds to walk past) independent of the number of items requiring delivery. When deciding how many houses to assign to a letter carrier, we need to estimate how much uncertainty there is in the time required to deliver mail to a lot of houses, in relation to the expected time required. (a) (1) For a given house, what is the probability that there are no items requiring delivery? (b) (2) What is the expected time taken by the letter carrier for a single house? (c) (3) What is the coefficient of variation of the time taken by the letter carrier for a single house? (d) (2) What is the expected time taken by the letter carrier for a street of 100 houses? (e) (2) What is the coefficient of variation of the time taken by the letter carrier for a street of 100 houses? (1) bonus mark for PLAN/DO/REPORT format